Question

What is the standard form of a polynomial `(y-2)(y^2+2y+3)`?

Answer 1

To transform this to the standard form we must first multiply each term in the left parenthesis by each term in the right parenthesis:
To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(y) - color(red)(2))(color(blue)(y^2) + color(blue)(2y) + color(blue)(3))` becomes:

`(color(red)(y) xx color(blue)(y^2)) + (color(red)(y) xx color(blue)(2y)) + (color(red)(y) xx color(blue)(3)) - (color(red)(2) xx color(blue)(y^2)) - (color(red)(2) xx color(blue)(2y)) - (color(red)(2) xx color(blue)(3))`

`y^3 + 2y^2 + 3y - 2y^2 - 4y - 6`

We can now group and combine like terms:

#y^3 + 2y^2 - 2y^2 + 3y - 4y - 6

`y^3 + (2 - 2)y^2 + (3 - 4)y - 6`

`y^3 + 0y^2 - 1y - 6`

`y^3 - y - 6`